Given $A=(2,5,1)$ and $B=(3,0,3)$, what are the parametric equations of a straight line passing between $A$ and $B$?
My attempt:
$$ \left\{ \begin{array}{c} x=2+t \\ y=5-5t \\ z=1+2t \end{array} \right. $$
and
$$ \left\{ \begin{array}{c} x=3-t \\ y=5t \\ z=3-2t \end{array} \right. $$
Yes that's correct they are both right!
The first is the equation from A to B $$\vec {OA}+t\vec {AB}$$
and the second is the equation from B to A $$\vec {OB}+t\vec {BA}$$